OTC 5L 7s

Omnitetrachordal MOS scale
5L+7s
12 tones (5+2+5)

MOS of the helmholtz / garibaldi / schismatic and superpyth temperaments, as well as Pythagorean. Very good 3/2 at almost any L/s ratio. Many modes may be pentachordally split in two ways. See also OTC 7L+5s.

P = 1.2600167527 (L=2187/2048, s=256/243)
Q = 7.9100586343 (2L+3.5s)

L = 100.00 to 240.00 cents (113.68 cents @ P, 203.91 cents @ Q)
s = 0.00 to 100.00 cents (90.23 cents @ P, 25.78 cents @ Q)

9/8 = L+s (200.00 to 240.00 cents)
4/3 = 2L+3s (480.00 to 500.00 cents)
generator = 4/3

notable EDOs: 17, 22, 27, 29, 41, 53, etc.

all modes:

Ls LsLss LsLss
sL sLssL sLssL		sLsLs sLsLs sL
Ls LssLs LssLs		LsLss LsLss Ls
sL ssLsL ssLsL		sLssL sLssL sL
Ls sLsLs sLsLs		LssLs LssLs Ls
		ssLsL ssLsL sL
	sLsLs sL sLsLs	sLsLs sLsLs Ls
	LsLss Ls LsLss
	sLssL sL sLssL
	LssLs Ls LssLs
	ssLsL sL ssLsL
sL sLsLs sLsLs	sLsLs Ls sLsLs

See also

• Omnitetrachordality
• Gallery of omnitetrachordal scales

References

• Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages 3685 and 10987.